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I want to add two IEEE 754 numbers. I followed the steps to add two 754 numbers. However the result it not correct. Number 1: S:0 E:01111111 M:11111111111111111111111

Number 2: S:0 E:01111111 M:00000000000000000000000

Here is my calculation:

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The site http://weitz.de/ieee/ gives this result: S: 0 E: 10000000 M: 10000000000000000000000

in my calculation the mantissa is 01111... Why?

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  • $\begingroup$ If you have more than 10 bits, it's very helpful to add a space between groups of four bits. $\endgroup$
    – gnasher729
    Aug 14, 2020 at 8:04
  • $\begingroup$ In their calculation I see the same mantissa as yours. $\endgroup$
    – plop
    Aug 14, 2020 at 11:16
  • $\begingroup$ What about number of bits & rounding? $\endgroup$
    – greybeard
    Aug 15, 2020 at 7:01
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    $\begingroup$ Just rounding. Tere is one extra 1 on the right of the mantissa, with rounding 01111... becomes 10000..... $\endgroup$
    – Grabul
    Sep 13, 2020 at 9:17
  • $\begingroup$ I’m voting to close this question because it is about one person making a mistake or misunderstanding something, and any answer would be completely useless for anyone else. Including OP who probably hasnt been stuck in this problem for three years. $\endgroup$
    – gnasher729
    Jan 28 at 16:51

2 Answers 2

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You forgot the implicit leading 1 in the mantissa. The mantissa is not 23 bits, it's 24 bits with a 1 as the leading bit.

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    $\begingroup$ i did not forgot it. 1,111... and 1,000 $\endgroup$
    – otto
    Aug 14, 2020 at 8:13
  • $\begingroup$ Where do these 1,111... and 1,000 come from ?? $\endgroup$
    – user16034
    Sep 5, 2022 at 13:46
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$$\begin{align}1&.01111111 \\+1&.11111111111111111111111\\=11&.01111110111111111111111\end{align}$$

You obtain the same result with the calculator.

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